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Such a is called a dissipative mapping taking X<\/jats:italic> to Y<\/jats:italic>. We also provide two different characterizations for the set of all dissipative mappings, and use them to characterize the unique dissipative mapping with minimal Frobenius norm. The minimal\u2010norm dissipative mapping is then used to determine the distance to asymptotic instability for dissipative\u2010Hamiltonian systems under general structure\u2010preserving perturbations. We illustrate our results over some numerical examples and compare them with those of Mehl, Mehrmann, and Sharma (Stability radii for linear Hamiltonian systems with dissipation under structure\u2010preserving perturbations, SIAM J Matrix Anal Appl<\/jats:italic>, 37(4):1625\u201354, 2016).<\/jats:p>","DOI":"10.1002\/nla.2402","type":"journal-article","created":{"date-parts":[[2021,7,14]],"date-time":"2021-07-14T08:32:33Z","timestamp":1626251553000},"update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Characterization of the dissipative mappings and their application to perturbations of dissipative\u2010Hamiltonian systems"],"prefix":"10.1002","volume":"28","author":[{"ORCID":"http:\/\/orcid.org\/0000-0002-2400-0457","authenticated-orcid":false,"given":"Mohit Kumar","family":"Baghel","sequence":"first","affiliation":[{"name":"Department of Mathematics Indian Institute of Technology Delhi Hauz Khas India"}]},{"ORCID":"http:\/\/orcid.org\/0000-0001-6423-6897","authenticated-orcid":false,"given":"Nicolas","family":"Gillis","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Operational Research University of Mons Mons Belgium"}]},{"ORCID":"http:\/\/orcid.org\/0000-0001-5110-4449","authenticated-orcid":false,"given":"Punit","family":"Sharma","sequence":"additional","affiliation":[{"name":"Department of Mathematics Indian Institute of Technology Delhi Hauz Khas India"}]}],"member":"311","published-online":{"date-parts":[[2021,7,14]]},"reference":[{"key":"e_1_2_10_2_1","doi-asserted-by":"publisher","DOI":"10.1137\/060657856"},{"key":"e_1_2_10_3_1","unstructured":"AdhikariB. 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